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Structural, mechanical and electronic properties of transition metal hydrides MH2 (M = Ti, Zr, Hf, Sc, Y, La, V and Cr)
Solid State Sciences 14 (2012) 583e586
Contents lists available at SciVerse ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Structural, mechanical and electronic properties of transition metal hydrides MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) T. Chihi a, *, M. Fatmi b, c, A. Bouhemadou a, d a
Laboratory for Development New Materials and their Characterization (LENMC), University Ferhat Abbas of Setif 19000, Algeria Research Unit on Emerging Materials (RUEM), University of Ferhat Abbas, Setif 19000, Algeria c Laboratory of Physics and Mechanics of Metallic Materials (LP3M), University of Ferhat Abbas, Setif 19000, Algeria d Department of Physics and Astronomy, College of Sciences, King Saud University, PO. Box 2455, Ryadh 11451, Saudi Arabia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 January 2012 Received in revised form 23 February 2012 Accepted 24 February 2012 Available online 3 March 2012
First-principles calculations have been carried out to investigate the structural, mechanic and electronic of transition metal hydrides MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr). It is found that TiH2 is mechanically unstable because of a negative C44 ¼ 21.31 GPa and C11eC12 < 0, the same behavior can be found in MH2 (M ¼ Zr, Hf, and Y) compounds. Also there is a strong interaction between M (Ti, Zr, Hf, Sc, Y, La, V and Cr) and H. On the other hand, the HeH bond orders are always negative or nil reason of brittleness. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Ab initio calculation Electronic structure Thermal properties
1. Introduction The convenient storage of hydrogen is tantamount to the convenient storage of energy. Thus, it is not surprising that most attention for the practical application of metal hydrides has focused on their potential as energy storage media. However, there are other possible applications, some of which are already in practice, albeit on a small scale [1]. In order to serve as a practical energy or hydrogen storage medium, a metal hydride must satisfy a number of criteria. Perhaps the most important is that it be easily formed and decomposed. Obviously, vary stable hydrides (e.g., ZrH2, TiH2, etc) are not suitable and we are limited ti those hydrides which will decompose at relatively low temperatures (300 C). Hydrogen is envisaged to be of great importance for future energy application, in particular, as an alternative fuel for both combustion engines and fuel cells [2]. It provides clean fuel that is environmentally very safe. Because hydrogen storage in liquid or gaseous forms imposes safety problems, metal hydrides offer a safe storage alternative and also have a higher volumetric density. Mg offers the highest maximum hydrogen capacity in all metal hydrides by far at 7.66 wt %, while VH2 offers 3.81wt%, but Mg is not
usable because it’s fully ionic and several works were devoted to improve on this such as by adding nickel [3]. There have been several investigations of the mechanical behavior of transition metal hydrides contained in their respective metal matrices [4e6]. A series of experiments [7e10] have been done by some scholars. Vanadium and its various hydrides were optimized and their total energies were also calculated by Peng et al. [11] using the local density functional theory. To understand the intrinsic mechanisms of alloying effects on the structural stability of vanadium hydrides, Matumura et al. [12] studied the electronic structure of VH2 and V2H containing various alloy elements with DV-Xa. By compressive loading at temperatures between room temperature and w500 C, the deformation behavior of bulk polycrystalline zirconium hydrides in the composition range ZrH1.60eZtH1.66 has been investigated [13]. In the present work we are interested in cubic MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds. They present a CaF2-type structure with a Fm3m space group. The paper is organized as follows. The computational method is described in Section 2. In Section 3, the results are presented and compared with available experimental and theoretical data. Conclusion is given in Section 4.
2. Computational method * Corresponding author. Fax: þ213 35 63 05 60. E-mail addresses: [email protected] (T. Chihi), [email protected] (M. Fatmi). 1293-2558/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2012.02.010
All calculations were performed by using the CASTEP (Cambridge Serial Total Energy Package) simulation program [14] that
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T. Chihi et al. / Solid State Sciences 14 (2012) 583e586
solves the Schrodinger-like KohneSham equations according to the formalism of the density functional theory (DFT) [15,16]. We used the Generalized Gradient Approximation (GGA), and a PerdewBurke-Ernzerhof (PBE) scheme [17], for handling the electronic exchange-correlation potential energy. Also, the pseudopotentials constructed using the ab initio normconserving scheme to describe the valence electron interaction with the atomic core, in which the Ti (3d24s2), Zr (4d25s2), Hf (4f145d26s2), Sc (3d14s2), Y (4d15s2), La (5d16s2), V (3d34s2), Cr (3d54s1) and H (1s1) orbitals are treated as valence electrons. Using for all structures high cut-off energy (330 eV) even at the price of spending long computational time is the condition to obtain accurate results. Brillouin zone (BZ) sampling is carried out using a 6 6 6 Monkhorst-Pack mesh set [18]. Atomic positions are relaxed and optimized within a density mixing scheme, based on a Conjugate Gradient (CG) method for eigenvalues minimization. Actually, the equilibrium lattice parameter is determined from a structural optimization, using the Broyden-Fletcher-Goldfarb-Shenno (BFGS) minimization technique. This technique provides a fast way of finding the lowest energy structure, with the following thresholds for converged structures: (i) energy change per atom less than 2 105 eV, (ii) residual force less than 0.05 eV/Å, (iii) atom displacement during geometry optimization less than 0.002 Å, and (iv) maximum stress within 0.1 GPa. The crystal structures are reported (Table 1). 3. Results and discussion 3.1. Structural properties The results for lattice parameters a are reported in Table 1 and compared with experimental and previous theoretical calculations. Our calculated value for lattice parameter a of MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds are in excellent agreement with the experimental data [19e23]. When comparing the results obtained within GGA, the computed lattice constant a deviates from the experimental one 2% for ZrH2, less than 2% for MH2 (M ¼ Ti, Sc, Y, La and V) and 6% for CrH2. For HfH2 we have not any experimental results for comparison. The relative deviation may be attributed to the fact that our calculation corresponds to perfect bulk material at zero temperature, whereas the experimental sample was synthesized at
Table 1 Calculated MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) structures: lattice parameters in Å; volumes in Å3; Z is the number of formula units in the unit cell, and the space group and compared with experimental data. Space group
a
TiH2
Fm3m
ZrH2
Fm3m
HfH2
Fm3m
ScH2
Fm3m
YH2
Fm3m
LaH2
Fm3m
VH2
Fm3m
CrH2
Fm3m
4.42 4.45a 4.87 4.77b 4.78 Xxxd 4.792 4.783c 5.298 5.209c 5.772 5.663a 4.224 4.271a,e 4.093 3.861a
a b c d e
Ref. Ref. Ref. Ref. Ref.
[19]. [20]. [21]. [22]. [23].
V
Z
86.83
4
115.95
4
109.51
4
110.07
4
148.72
4
192.38
4
75.37
4
68.58
4
high temperature. The total energies of MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds are in Table 3 should be used to derive the stability by subtracting for each MH2 the energy of M and twice the energy of H to get the stability. On the other hand, the total energies (stability) of MH2 (M ¼ Sc, Ti, V, and Cr) [MH2 (M ¼ Sc, Y and La)] compounds decrease, the nearest-neighbor distance DMeM and DMeH in these compounds decrease [increase] and the bulk modulus increase [decrease] for M metals in the same row [column] in the Periodic Table, with increasing atomic number as shown in Table 2. To the best of our knowledge, no experimental data are yet available for those compounds, so that our results can be considered as prediction for future investigations. 3.2. Elastic constants The elastic constants of solids provide a link between mechanical and dynamical behaviors of crystals, and give important information concerning the nature of forces operating in solids. In particular, they provide information on stability and stiffness of materials. It is well known that first-order and second-order derivatives of the potential give forces and elastic constants. Therefore, it is an important issue to check the accuracy of the calculations for forces and elastic constants. Let us recall here that pressure effect upon elastic constants is essential, at least for understanding interatomic interactions, mechanical stability and phase transition mechanism. For a cubic crystal, the generalized elastic stability criteria in terms of elastic constants [24]:
ðC11 þ 2C12 Þ=3>0 ðC11 C12 Þ=2>0
C44 >0
For MH2 (M ¼ Sc, La, V and Cr) compounds these criteria are satisfied in the studied pressure Table 3. TiH2 is also mechanically unstable because of a negative C44 ¼ 21.31 GPa and C11eC12 < 0, the same behavior can be found in MH2 (M ¼ Zr, Hf, and Y) compounds. 3.3. Electronic structures DFT band structure calculations are conducted to understand the electronic structure of different materials. The role of hydrogen can be analyzed in terms of modifications of crystallographic data (volume effect, structural modification, elastic properties) and chemical bonding effects (HeH and HeM interaction, band energy filling, and electronic modification at the Fermi level .). Fig. 1 shows the partial s-, p-, and d-Densities of States (DOS) for all MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds. The Fermi level is taken to be of zero energy, thus the energy scale is not absolute in this calculation. We show here only the vicinity of the Fermi energy level. The peaks corresponding to the lowest energy (not shown) are due to the contribution M-s and M-p for all compounds. The total-density of states (TDOS) for all MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds is shown in Fig. 1. The TDOS at the Fermi level Ef (N(Ef)) for all MH2 compounds is listed in Table 2. Near the Fermi level, the DOS mainly originates from the M-d states (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr), this suggests that our compounds are all Table 2 Distances between nearest-neighbored atoms and energy Fermi level of MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds studied in this work.
Ef DMeM DMeH
TiH2
ZrH2
HfH2
ScH2
YH2
LaH2
VH2
CrH2
6.720 3.131 1.918
5.703 3.448 2.111
4.865 3.383 2.072
4.569 3.389 2.075
4.686 3.746 2.294
5.382 4.082 2.500
6.096 2.987 1.829
8.234 2.894 1.772
T. Chihi et al. / Solid State Sciences 14 (2012) 583e586
585
Table 3 Formation energy E in (eV), zero pressure elastic moduli (Cij) in GPa of cubic MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr). The polycrystalline bulk moduli (B), shear moduli (G), Young’s moduli (Y), and Poisson’s ratio n were obtained using the Voigt approximation. All the elastic constants are in GPa except for the dimensionless n. Material
E
C11
C12
C44
B
G
B/G
Y
n
TiH2 ZrH2 HfH2 ScH2 YH2 LaH2 VH2 CrH2
6545 5258 1766 5243 906 3584 8035 9996
108.43 100.99 110.99 105.17 72.13 76.31 278.81 334.05
150.08 119.31 159.09 85.26 80.45 46.38 103.95 116.82
21.31 34.71 20.57 93.20 56.81 48.73 88.28 114.13
136.20 113.21 143.06 91.90 77.67 56.36 162.24 189.23
21.11 17.16 2.72 59.90 32.42 35.22 87.94 111.92
6.45 6.59 52.60 1.53 2.39 1.60 1.84 1.69
65.41 28.24 76.42 28.83 12.70 41.23 222.35 273.52
0.580 0.541 0.589 0.447 0.527 0.378 0.271 0.259
conductive, and the d bands of the transition metal play the dominant role in electrical transport. The DOS of all MH2 can be mainly divided into two parts in the valence bonding region. The first one extended between about 12.55 eV and 1.70 eV is the combination of H-s, M-d and with a small M-s and (or) M-p states, and it is mainly the contribution of H-s states; the second part from about 1.70 eV to 0 eV is due to the contribution of M-d, M-p and Ms states. The first conduction band located between 0 eV and 7.5 eV is mainly composed of M-d, M-p and M-s with a small H-s states. There are two interesting features observed from Fig. 1: (1) As M from Hf, Ti to Zr, the peaks of H-s states hybridized of M-d states
shift toward lower energy levels. This indicates that the covalent interaction M-d and H-s states weakens, which resulted in the decrease of bulk modulus (B) for MH2 as M ¼ Hf, Ti, Zr respectively. The same behavior can be found for MH2 as M ¼ Sc, Y, La respectively (MH2 as M ¼ Cr, V, Ti, Sc respectively), in the same column (in the same period) of the periodic table. (2) The electronic states around the Fermi level for all compounds and at the top of valence bands are dominated by M-d. Lower conduction bands are mainly due to M-d states. Let us mention a large DOS at the Fermi level (Table 2), implying a high electronic conductivity and various applications to electronic conductors.
Fig. 1. Partial state densities for MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) structures. The Fermi energy is set to zero.
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T. Chihi et al. / Solid State Sciences 14 (2012) 583e586
other hand, the HeH bond orders are always negative or nil reason of brittleness.
Table 4 Bond orders in the MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) structures.
HeH HeM
TiH2
ZrH2
HfH2
ScH2
YH2
LaH
VH2
CrH2
0.04 0.09
0.03 0.10
0.01 0.13
0.06 0.12
0.02 0.14
0.02 0.11
0.02 0.07
0.00 0.09
3.4. Bond orders between atoms Bond order is the overlap population of electrons between atoms, and this is a measure of the strength of the covalent bond between atoms. In Table 4., if the overlap population is positive (þ) a bonding-type interaction is operating between atom, whereas if it is negative () an anti-bonding-type interaction is dominant between atoms. It is apparent that the bonding-type interactions are operating between the M (Ti, Zr, Hf, Sc, Y, La, V and Cr) (3d, 4d and 5d) and the H 1s electrons. Thus, there is a strong interaction between M (Ti, Zr, Hf, Sc, Y, La, V and Cr) and H. On the other hand, the HeH bond orders are always negative or nil reason of brittleness. 4. Summary and conclusion Using the Pseudo Potential-Plane wave method based on the Density Functional Theory, within a Generalized Gradient Approximation. A detailed study has been reported on structural, elastic and electronic of transition metal hydrides MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr). TiH2 is mechanically unstable because of a negative C44 ¼ 21.31 GPa and C11eC12 < 0, the same behavior can be found in MH2 (M ¼ Zr, Hf, and Y) compounds. There is a strong interaction between M (Ti, Zr, Hf, Sc, Y, La, V and Cr) and H. On the
References [1] J. J. Reilly, Department of Energy and Environment Brookhaven National Laboratory Upton, New York, 11973, February 1979. [2] T. Klassen, W. Oelerich, K. Zeng, R. Bormann, Nanocrystalline Mg Based Alloys for Hydrogen Storage, GKSS-Forschungszentrun Geesthacht GmbH, 1998, P. 11. [3] R. Bowman, B. Fultz, Metallic hydrides I: hydrogen storage and other gGas phase applications, MRS Bull. (September 2002). [4] C.J. Beevers, M.R. Warren, D.V. Edmonds, J. Less Comm. Met 14 (1968) 387. [5] G.W. Parry, W. Evans, Electrochem. Tech. 4 (1966) 225. [6] M.R. Warren, C.J. Beevers, Met. Sci. J. 1 (1967) 173. [7] N. Budylkin, L. Voloschin, E. Mironova, J. Alloy. Compd 1160 (1996) 233. [8] R. Dus, E. Nowicka, Z. Wolfram, J. Alloy. Compd 496 (1997) 253. [9] D. Yamashita, K. Komiya, Yukawa, J. Alloy. Compd 137 (2004) 364. [10] A.L. Buzlukov, A.V. Skripov, J. Alloy. Compd 61 (2004) 366. [11] S.M. Peng, J.P. Zhao, M.N. Yang, S.J. Yao, S.Z. Luo, Z.L. Xu, Atom. Ener. Sci. Tech. 469 (2000) 34. [12] T. Matumura, H. Yukawa, M. Morinaga, J. Alloy. Compd 82 (1999) 248. [13] K.G. Barraclough, C.J. Beevers, J. Materials Science 4 (1969) 518. [14] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. pickard, P.J. Haspin, S.J. Clark, M.C. Payne, J. Phys. Condens. Matter 14 (2002) 2717. [15] P. Hohenberg, W. Kohn, Phys. Rev. B 13 (6) (1964) 864. [16] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 113. [17] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 78 (1997) 1396. [18] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [19] K.M. Makkay, Hydrogen Compounds of the Metallic Elements, Spon Ltd, London, 1966. [20] S.S. Sidhu, J.C. McGuire, J. Appl. Phys. 23 (1952) 1257. [21] W.M. Mueller, in: W.M. Mueller, J.P. Blackledge, G.G. Libowitz (Eds.), Hydrides of REM in Metal Hydrides, Academic Press, New York, 1968. [22] R. L. Beck and W. M. Mueller, Hydrides of Zr and Hf, ibid. [23] T. Matumura, H. Yukawa, M. Morinaga, J. Alloys Compd 284 (1999) 82. [24] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon, Oxford, 1956.
Contents lists available at SciVerse ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Structural, mechanical and electronic properties of transition metal hydrides MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) T. Chihi a, *, M. Fatmi b, c, A. Bouhemadou a, d a
Laboratory for Development New Materials and their Characterization (LENMC), University Ferhat Abbas of Setif 19000, Algeria Research Unit on Emerging Materials (RUEM), University of Ferhat Abbas, Setif 19000, Algeria c Laboratory of Physics and Mechanics of Metallic Materials (LP3M), University of Ferhat Abbas, Setif 19000, Algeria d Department of Physics and Astronomy, College of Sciences, King Saud University, PO. Box 2455, Ryadh 11451, Saudi Arabia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 January 2012 Received in revised form 23 February 2012 Accepted 24 February 2012 Available online 3 March 2012
First-principles calculations have been carried out to investigate the structural, mechanic and electronic of transition metal hydrides MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr). It is found that TiH2 is mechanically unstable because of a negative C44 ¼ 21.31 GPa and C11eC12 < 0, the same behavior can be found in MH2 (M ¼ Zr, Hf, and Y) compounds. Also there is a strong interaction between M (Ti, Zr, Hf, Sc, Y, La, V and Cr) and H. On the other hand, the HeH bond orders are always negative or nil reason of brittleness. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Ab initio calculation Electronic structure Thermal properties
1. Introduction The convenient storage of hydrogen is tantamount to the convenient storage of energy. Thus, it is not surprising that most attention for the practical application of metal hydrides has focused on their potential as energy storage media. However, there are other possible applications, some of which are already in practice, albeit on a small scale [1]. In order to serve as a practical energy or hydrogen storage medium, a metal hydride must satisfy a number of criteria. Perhaps the most important is that it be easily formed and decomposed. Obviously, vary stable hydrides (e.g., ZrH2, TiH2, etc) are not suitable and we are limited ti those hydrides which will decompose at relatively low temperatures (300 C). Hydrogen is envisaged to be of great importance for future energy application, in particular, as an alternative fuel for both combustion engines and fuel cells [2]. It provides clean fuel that is environmentally very safe. Because hydrogen storage in liquid or gaseous forms imposes safety problems, metal hydrides offer a safe storage alternative and also have a higher volumetric density. Mg offers the highest maximum hydrogen capacity in all metal hydrides by far at 7.66 wt %, while VH2 offers 3.81wt%, but Mg is not
usable because it’s fully ionic and several works were devoted to improve on this such as by adding nickel [3]. There have been several investigations of the mechanical behavior of transition metal hydrides contained in their respective metal matrices [4e6]. A series of experiments [7e10] have been done by some scholars. Vanadium and its various hydrides were optimized and their total energies were also calculated by Peng et al. [11] using the local density functional theory. To understand the intrinsic mechanisms of alloying effects on the structural stability of vanadium hydrides, Matumura et al. [12] studied the electronic structure of VH2 and V2H containing various alloy elements with DV-Xa. By compressive loading at temperatures between room temperature and w500 C, the deformation behavior of bulk polycrystalline zirconium hydrides in the composition range ZrH1.60eZtH1.66 has been investigated [13]. In the present work we are interested in cubic MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds. They present a CaF2-type structure with a Fm3m space group. The paper is organized as follows. The computational method is described in Section 2. In Section 3, the results are presented and compared with available experimental and theoretical data. Conclusion is given in Section 4.
2. Computational method * Corresponding author. Fax: þ213 35 63 05 60. E-mail addresses: [email protected] (T. Chihi), [email protected] (M. Fatmi). 1293-2558/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2012.02.010
All calculations were performed by using the CASTEP (Cambridge Serial Total Energy Package) simulation program [14] that
584
T. Chihi et al. / Solid State Sciences 14 (2012) 583e586
solves the Schrodinger-like KohneSham equations according to the formalism of the density functional theory (DFT) [15,16]. We used the Generalized Gradient Approximation (GGA), and a PerdewBurke-Ernzerhof (PBE) scheme [17], for handling the electronic exchange-correlation potential energy. Also, the pseudopotentials constructed using the ab initio normconserving scheme to describe the valence electron interaction with the atomic core, in which the Ti (3d24s2), Zr (4d25s2), Hf (4f145d26s2), Sc (3d14s2), Y (4d15s2), La (5d16s2), V (3d34s2), Cr (3d54s1) and H (1s1) orbitals are treated as valence electrons. Using for all structures high cut-off energy (330 eV) even at the price of spending long computational time is the condition to obtain accurate results. Brillouin zone (BZ) sampling is carried out using a 6 6 6 Monkhorst-Pack mesh set [18]. Atomic positions are relaxed and optimized within a density mixing scheme, based on a Conjugate Gradient (CG) method for eigenvalues minimization. Actually, the equilibrium lattice parameter is determined from a structural optimization, using the Broyden-Fletcher-Goldfarb-Shenno (BFGS) minimization technique. This technique provides a fast way of finding the lowest energy structure, with the following thresholds for converged structures: (i) energy change per atom less than 2 105 eV, (ii) residual force less than 0.05 eV/Å, (iii) atom displacement during geometry optimization less than 0.002 Å, and (iv) maximum stress within 0.1 GPa. The crystal structures are reported (Table 1). 3. Results and discussion 3.1. Structural properties The results for lattice parameters a are reported in Table 1 and compared with experimental and previous theoretical calculations. Our calculated value for lattice parameter a of MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds are in excellent agreement with the experimental data [19e23]. When comparing the results obtained within GGA, the computed lattice constant a deviates from the experimental one 2% for ZrH2, less than 2% for MH2 (M ¼ Ti, Sc, Y, La and V) and 6% for CrH2. For HfH2 we have not any experimental results for comparison. The relative deviation may be attributed to the fact that our calculation corresponds to perfect bulk material at zero temperature, whereas the experimental sample was synthesized at
Table 1 Calculated MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) structures: lattice parameters in Å; volumes in Å3; Z is the number of formula units in the unit cell, and the space group and compared with experimental data. Space group
a
TiH2
Fm3m
ZrH2
Fm3m
HfH2
Fm3m
ScH2
Fm3m
YH2
Fm3m
LaH2
Fm3m
VH2
Fm3m
CrH2
Fm3m
4.42 4.45a 4.87 4.77b 4.78 Xxxd 4.792 4.783c 5.298 5.209c 5.772 5.663a 4.224 4.271a,e 4.093 3.861a
a b c d e
Ref. Ref. Ref. Ref. Ref.
[19]. [20]. [21]. [22]. [23].
V
Z
86.83
4
115.95
4
109.51
4
110.07
4
148.72
4
192.38
4
75.37
4
68.58
4
high temperature. The total energies of MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds are in Table 3 should be used to derive the stability by subtracting for each MH2 the energy of M and twice the energy of H to get the stability. On the other hand, the total energies (stability) of MH2 (M ¼ Sc, Ti, V, and Cr) [MH2 (M ¼ Sc, Y and La)] compounds decrease, the nearest-neighbor distance DMeM and DMeH in these compounds decrease [increase] and the bulk modulus increase [decrease] for M metals in the same row [column] in the Periodic Table, with increasing atomic number as shown in Table 2. To the best of our knowledge, no experimental data are yet available for those compounds, so that our results can be considered as prediction for future investigations. 3.2. Elastic constants The elastic constants of solids provide a link between mechanical and dynamical behaviors of crystals, and give important information concerning the nature of forces operating in solids. In particular, they provide information on stability and stiffness of materials. It is well known that first-order and second-order derivatives of the potential give forces and elastic constants. Therefore, it is an important issue to check the accuracy of the calculations for forces and elastic constants. Let us recall here that pressure effect upon elastic constants is essential, at least for understanding interatomic interactions, mechanical stability and phase transition mechanism. For a cubic crystal, the generalized elastic stability criteria in terms of elastic constants [24]:
ðC11 þ 2C12 Þ=3>0 ðC11 C12 Þ=2>0
C44 >0
For MH2 (M ¼ Sc, La, V and Cr) compounds these criteria are satisfied in the studied pressure Table 3. TiH2 is also mechanically unstable because of a negative C44 ¼ 21.31 GPa and C11eC12 < 0, the same behavior can be found in MH2 (M ¼ Zr, Hf, and Y) compounds. 3.3. Electronic structures DFT band structure calculations are conducted to understand the electronic structure of different materials. The role of hydrogen can be analyzed in terms of modifications of crystallographic data (volume effect, structural modification, elastic properties) and chemical bonding effects (HeH and HeM interaction, band energy filling, and electronic modification at the Fermi level .). Fig. 1 shows the partial s-, p-, and d-Densities of States (DOS) for all MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds. The Fermi level is taken to be of zero energy, thus the energy scale is not absolute in this calculation. We show here only the vicinity of the Fermi energy level. The peaks corresponding to the lowest energy (not shown) are due to the contribution M-s and M-p for all compounds. The total-density of states (TDOS) for all MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds is shown in Fig. 1. The TDOS at the Fermi level Ef (N(Ef)) for all MH2 compounds is listed in Table 2. Near the Fermi level, the DOS mainly originates from the M-d states (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr), this suggests that our compounds are all Table 2 Distances between nearest-neighbored atoms and energy Fermi level of MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) compounds studied in this work.
Ef DMeM DMeH
TiH2
ZrH2
HfH2
ScH2
YH2
LaH2
VH2
CrH2
6.720 3.131 1.918
5.703 3.448 2.111
4.865 3.383 2.072
4.569 3.389 2.075
4.686 3.746 2.294
5.382 4.082 2.500
6.096 2.987 1.829
8.234 2.894 1.772
T. Chihi et al. / Solid State Sciences 14 (2012) 583e586
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Table 3 Formation energy E in (eV), zero pressure elastic moduli (Cij) in GPa of cubic MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr). The polycrystalline bulk moduli (B), shear moduli (G), Young’s moduli (Y), and Poisson’s ratio n were obtained using the Voigt approximation. All the elastic constants are in GPa except for the dimensionless n. Material
E
C11
C12
C44
B
G
B/G
Y
n
TiH2 ZrH2 HfH2 ScH2 YH2 LaH2 VH2 CrH2
6545 5258 1766 5243 906 3584 8035 9996
108.43 100.99 110.99 105.17 72.13 76.31 278.81 334.05
150.08 119.31 159.09 85.26 80.45 46.38 103.95 116.82
21.31 34.71 20.57 93.20 56.81 48.73 88.28 114.13
136.20 113.21 143.06 91.90 77.67 56.36 162.24 189.23
21.11 17.16 2.72 59.90 32.42 35.22 87.94 111.92
6.45 6.59 52.60 1.53 2.39 1.60 1.84 1.69
65.41 28.24 76.42 28.83 12.70 41.23 222.35 273.52
0.580 0.541 0.589 0.447 0.527 0.378 0.271 0.259
conductive, and the d bands of the transition metal play the dominant role in electrical transport. The DOS of all MH2 can be mainly divided into two parts in the valence bonding region. The first one extended between about 12.55 eV and 1.70 eV is the combination of H-s, M-d and with a small M-s and (or) M-p states, and it is mainly the contribution of H-s states; the second part from about 1.70 eV to 0 eV is due to the contribution of M-d, M-p and Ms states. The first conduction band located between 0 eV and 7.5 eV is mainly composed of M-d, M-p and M-s with a small H-s states. There are two interesting features observed from Fig. 1: (1) As M from Hf, Ti to Zr, the peaks of H-s states hybridized of M-d states
shift toward lower energy levels. This indicates that the covalent interaction M-d and H-s states weakens, which resulted in the decrease of bulk modulus (B) for MH2 as M ¼ Hf, Ti, Zr respectively. The same behavior can be found for MH2 as M ¼ Sc, Y, La respectively (MH2 as M ¼ Cr, V, Ti, Sc respectively), in the same column (in the same period) of the periodic table. (2) The electronic states around the Fermi level for all compounds and at the top of valence bands are dominated by M-d. Lower conduction bands are mainly due to M-d states. Let us mention a large DOS at the Fermi level (Table 2), implying a high electronic conductivity and various applications to electronic conductors.
Fig. 1. Partial state densities for MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) structures. The Fermi energy is set to zero.
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other hand, the HeH bond orders are always negative or nil reason of brittleness.
Table 4 Bond orders in the MH2 (Ti, Zr, Hf, Sc, Y, La, V and Cr) structures.
HeH HeM
TiH2
ZrH2
HfH2
ScH2
YH2
LaH
VH2
CrH2
0.04 0.09
0.03 0.10
0.01 0.13
0.06 0.12
0.02 0.14
0.02 0.11
0.02 0.07
0.00 0.09
3.4. Bond orders between atoms Bond order is the overlap population of electrons between atoms, and this is a measure of the strength of the covalent bond between atoms. In Table 4., if the overlap population is positive (þ) a bonding-type interaction is operating between atom, whereas if it is negative () an anti-bonding-type interaction is dominant between atoms. It is apparent that the bonding-type interactions are operating between the M (Ti, Zr, Hf, Sc, Y, La, V and Cr) (3d, 4d and 5d) and the H 1s electrons. Thus, there is a strong interaction between M (Ti, Zr, Hf, Sc, Y, La, V and Cr) and H. On the other hand, the HeH bond orders are always negative or nil reason of brittleness. 4. Summary and conclusion Using the Pseudo Potential-Plane wave method based on the Density Functional Theory, within a Generalized Gradient Approximation. A detailed study has been reported on structural, elastic and electronic of transition metal hydrides MH2 (M ¼ Ti, Zr, Hf, Sc, Y, La, V and Cr). TiH2 is mechanically unstable because of a negative C44 ¼ 21.31 GPa and C11eC12 < 0, the same behavior can be found in MH2 (M ¼ Zr, Hf, and Y) compounds. There is a strong interaction between M (Ti, Zr, Hf, Sc, Y, La, V and Cr) and H. On the
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